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If n and y are positive integers and 450y=n^3, which of the

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Manager
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If n and y are positive integers and 450y=n^3, which of the [#permalink] New post 04 Apr 2006, 01:30
If n and y are positive integers and 450y=n^3, which of the following must be an integer?

I. y/3*2^2*5

II. y/3^2*2*5

III. y/3*2*5^2

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Manager
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 [#permalink] New post 04 Apr 2006, 08:08
450y = n^3
2*3^2*5^2 y = n^3
So if both n and y are integers, we need to have a look
at what the least y could be so that 450 y = n^3.

The least possible y is 2^2*3*5, cause these are the
missing parts so that a third cube out of the term could
lead to an integer (--> n).

450 * 2^2*3*5 = (2*3*5)^3

So even in this case, y is divisible by 2^2*3*5.

So the answer is I.
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 [#permalink] New post 04 Apr 2006, 10:09
Good explanation ccax

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  [#permalink] 04 Apr 2006, 10:09
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If n and y are positive integers and 450y=n^3, which of the

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